This: and
this says it better than I could (and with pictures).
Basically you need some LECA and some pots with two wholes drilled 1-1.5 up on the side. LECA has many different brand names such as Hydroton, Primeagra etc. but I don't find the brand matters
that much. There are definitely diffrences between brands but that is a whole 'nother thread.
Fertilizer is up to you. Lots of people use MSU or K-lite but pretty much any good orchid fertilizer is going to be fine. So long as it's a complete fertilizer with calcium and magnesium you should be ok. If it doesn't have Ca and Mg it wasn't a good orchid fertilizer in the first place.
A heat mat, like ones used to start seedlings indoors, will certainly speed the adaptation process up but isn't strictly necessary. I have a heat mat but have never used it on the orchids I've switched.
As mentioned before, timing is absolutely key. I would not switch anything that isn't actively growing roots, this means you can see the white root tips. I think this gets overlooked a lot, and I can say when I started I definitely ignored this. To put it plainly actively growing roots=easy transition, no growing roots= possible failure, no/little roots=probable failure. Obviously there are always exceptions but this has been my experience with SH.